A New Inequality Measure that is Sensitive to Extreme Values and Asymmetries

Tinbergen Institute Discussion Paper 2017-102/III

36 Pages Posted: 6 Nov 2017

See all articles by Michael McAleer

Michael McAleer

Erasmus University Rotterdam - Erasmus School of Economics, Econometric Institute; Tinbergen Institute; University of Tokyo - Centre for International Research on the Japanese Economy (CIRJE), Faculty of Economics

Hang K. Ryu

Chung-Ang University - Department of Economics

Daniel J. Slottje

Southern Methodist University (SMU) - Department of Economics

Date Written: November 3, 2017

Abstract

There is a vast literature on the selection of an appropriate index of income inequality and on what desirable properties such a measure (or index) should contain. The Gini index is, of course, the most popular. There is a concurrent literature on the use of hypothetical statistical distributions to approximate and describe an observed distribution of incomes. Pareto and others observed early on that incomes tend to be heavily right-tailed in their distribution. These asymmetries led to approximating the observed income distributions with extreme value hypothetical statistical distributions, such as the Pareto distribution. But these income distribution functions (IDFs) continue to be described with a single index (such as the Gini) that poorly detect the extreme values present in the underlying empirical IDF. This paper introduces a new inequality measure to supplement, but not to replace, the Gini that measures more accurately the inherent asymmetries and extreme values that are present in observed income distributions. The new measure is based on a third-order term of a Legendre polynomial from the logarithm of a share function (or Lorenz curve). We advocate using the two measures together to provide a better description.

Keywords: Inequality Index, Extreme value distributions, Maximum entropy method, Orthonormal basis, Legendre polynomials

JEL Classification: D31, D63

Suggested Citation

McAleer, Michael and Ryu, Hang K. and Slottje, Daniel J., A New Inequality Measure that is Sensitive to Extreme Values and Asymmetries (November 3, 2017). Tinbergen Institute Discussion Paper 2017-102/III. Available at SSRN: https://ssrn.com/abstract=3064717 or http://dx.doi.org/10.2139/ssrn.3064717

Michael McAleer (Contact Author)

Erasmus University Rotterdam - Erasmus School of Economics, Econometric Institute ( email )

Rotterdam
Netherlands

Tinbergen Institute

Rotterdam
Netherlands

University of Tokyo - Centre for International Research on the Japanese Economy (CIRJE), Faculty of Economics

Tokyo
Japan

Hang K. Ryu

Chung-Ang University - Department of Economics ( email )

Seoul
Korea

Daniel J. Slottje

Southern Methodist University (SMU) - Department of Economics ( email )

Dallas, TX 75275
United States

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